Rate of Change of Diffraction Pattern with Increasing Distance Between Slits

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In summary, the conversation discusses monochromatic electromagnetic radiation falling on double slits and creating a diffraction pattern on a screen. It then introduces the concept of the distance between the slits increasing at a constant rate, and asks for the rate at which the distance between the central maximum and first maximum changes. The solution involves using the equation x = nλL/d and finding dx/dt by taking the derivative of this equation with respect to time. The value of dd/dt is given as x μm/s, and the distance between the slits is denoted as d μm.
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Homework Statement


Monochromatic electromagnetic radiation of wavelength λ nm falls on double slits, creating a diffraction pattern on a screen L m away, Suppose now that the distance between the slits begins to increase at a constant rate:

dd/dt = x μm/s.

Assume that everything else remains unchanged. Find the rate at which the distance between the central maximum and first maximum is changing, in cm/s, at the instant the distance between the slits is d μm

Homework Equations


x = nλL/d

3. The Attempt at a Solution
x = λL/d
dx/dt = (λL/d) * (1/ dd/dt) is this right? I am confused about dd/dt part.
 
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  • #2
I think you want d (1/d) / dt.
 

FAQ: Rate of Change of Diffraction Pattern with Increasing Distance Between Slits

What is monochromatic diffraction?

Monochromatic diffraction is the phenomenon where a monochromatic (single wavelength) light wave is bent or spread out as it passes through a narrow slit or around an obstacle.

What causes monochromatic diffraction?

Monochromatic diffraction is caused by the interference of the light waves as they pass through the slit or around the obstacle. This interference results in a pattern of bright and dark fringes on a screen placed behind the slit or obstacle.

How is monochromatic diffraction different from other types of diffraction?

Monochromatic diffraction differs from other types of diffraction (such as chromatic or polychromatic diffraction) in that it involves only one wavelength of light. This results in a simpler and more predictable diffraction pattern.

What is the significance of monochromatic diffraction in science and technology?

Monochromatic diffraction is important in many scientific and technological fields, including optics, spectroscopy, and crystallography. It allows scientists to study the properties of light and materials, and is used in various applications such as in lasers, microscopes, and diffraction gratings.

How can monochromatic diffraction be controlled or manipulated?

The diffraction pattern produced by monochromatic diffraction can be controlled and manipulated by changing the size and shape of the slit or obstacle, as well as the distance between the slit or obstacle and the screen. Additionally, using different wavelengths of light or adjusting the intensity of the light source can also affect the diffraction pattern.

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